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Differentiating the Area of a Circle

  1. Nov 29, 2013 #1

    S.R

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    In my high school Calculus course, I've encountered several optimization problems involving the area of a circle and I noticed the obvious fact that if you differentiate the area of a circle you obtain the expression for its circumference. This implies that the rate of change of a circle's area is equal to its circumference (which is difficult to visualize). So what does notion actually mean?

    S.R
     
  2. jcsd
  3. Nov 29, 2013 #2

    tiny-tim

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    Hi S.R! :smile:

    It means that the whole area is made of lots of little circumferences …

    if you subtract one area from a slightly larger one, you get a circumference. :wink:

    (works for spheres also!)
     
  4. Nov 29, 2013 #3

    S.R

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    Oh :D Essentially the area consists of concentric circles?
     
  5. Nov 29, 2013 #4

    tiny-tim

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